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Introduction to Geometry of Manifolds with Symmetry

  • Book
  • © 1994

Overview

Authors:
  1. V. V. Trofimov

    1. Department of Geometry and Topology, Moscow State University, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 270)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Elements of Differential Geometry

    • V. V. Trofimov
    Pages 1-80

  3. Lie Groups and Lie Algebras

    • V. V. Trofimov
    Pages 81-162

  4. Symmetric Spaces

    • V. V. Trofimov
    Pages 163-224

  5. Smooth Vector Bundles and Characteristic Classes

    • V. V. Trofimov
    Pages 225-278

  6. Applications

    • V. V. Trofimov
    Pages 279-319

  7. Back Matter

    Pages 321-328
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Keywords

About this book

One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour­ dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.

Authors and Affiliations

  • Department of Geometry and Topology, Moscow State University, Moscow, Russia

    V. V. Trofimov

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